随机Hill方程基态eigenvalue密度的形状
On the shape of the ground state eigenvalue density of a random Hill's equation
摘要：
考虑希尔算子$Q = - d^2/dx^2 + q(x)$，其中$q(x)$，$0 \le x \le 1$，是白噪声。用$f(μ)$表示$-λ_0(q)$的概率密度函数，即基态本征值的负值，在$μ$处。我们将该密度的详细渐近性描述为$μ\to +\infty$。这一结果是基于对S. Cambronero和H.P. McKean。
英文摘要：
Consider the Hill's operator $Q = - d^2/dx^2 + q(x)$ in which $q(x)$, $0 \le x \le 1$, is a White Noise. Denote by $f(μ)$ the probability density function of $-λ_0(q)$, the negative of the ground state eigenvalue, at $μ$. We describe the detailed asymptotics of this density as $μ\to +\infty$. This result is based on a precise Laplace analysis of a functional integral representation for $f(μ)$ established by S. Cambronero and H.P. McKean.
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